Chapter 10: Tides

Chapter 10: TidesRemember that tides are waves that are causedby the gravitational attraction of moon and sun.Tidal waves are the longest of all waves, L canbe up to half the Earth’s circumference.Fig. 9-2Waves are created by a ‘disturbance’.* wind (wind waves, L 60-150 m), where most of ocean’s wave energy is located.* earthquakes (seismic waves, L 200 km)* sun/moon (tidal waves, planetary scale).Restoring force is*gravity (gravity waves).*surface tension (capillary waves)Tides:Tides1. Understanding the Earth-Moon systemThe Earth-Moon system revolves as a system once a month aroundits center of mass. The center of mass of both systems is located insidethe earth (about one quarter of earth’s radius below the surface of theearth). It is called the barycenter.Fig. 10-1aCentrifugal force2. Understandingcentripedal andcentrifugal forceFig. 10-1bCentripedal force is the force that keeps the moon (ball)in a stable orbit around the earth (person) and counterweighsthe centrifugal force, just has the opposite direction. For astable orbit both need to be in balance.

Tides:3. Understanding gravityWhat causes tides?Tides: 2. Understanding gravityTides are created by the imbalancebetween two forces:1. Gravitational force of the Moon and Sunon Earth Newton’s universal law of gravitation: Every particle of mass in the universe attracts every otherparticle of mass. Gravitational force is proportional to themass of both bodies and inversely to square of the distancebetween the 2 bodies.Gravitational forces on Earthdue to the MoonIf mass increases (½), then gravitational forceincreases (½)If distance increases (½), then gravitationalforce greatly decreases (¾¾)2. Centripetal (center-seeking) forcerequired to keep bodies in nearly circularorbitsCentripetal forces on Earth dueto the Moon Force is thesameeverywhereon Earth Forcedecreaseswithincreasingdistance Force isdirectedtoward theMoon’scenter ofmass Force isdirectedperpendicularto Earth’scentereverywhereon Earth10-310-5

Resultantforces are:– Thedifferencebetweengravitational(G) andcentripetal(C) forces– Directedaway fromMoon on theside of EarthoppositeMoon– Directedtoward Moonon the sideof EarthThe samedirection andmagnitude of thecentripedal forceis required tohold objects intheir orbitalpaths.10-4Tide-generating forces Tidegeneratingforces are thehorizontalcomponent ofthe resultantforce Maximizedalong a“latitude” of45º relative tothe “equator”between thezenith andnadir Figure 10-7Tide-generatingforces produce2 bulges:1.Away fromMoon on sideof Earthopposite Moon2.Toward Moonon side of Earthfacing MoonEarth rotatesinto and out oftidal bulges,creating highand low tidesResultant forcesFigure 10-6Tidal bulgesFigure 10-8‘Idealized tidal theory’

The lunar day Tidal bulges follow Moon as it rotates aroundEarth Lunar day is 50 minutes longer than a solar daybecause the Moon is moving in its orbit aroundEarth ( lunar cycle is 29.5 days long)Figure 10-9Why46%?The influence of the Sun The Sun ismuch moremassive thanthe Moon butmuch furtheraway Solar bulgesare 46% thesize of lunarbulgesFigure 10-10The monthly tidal cycle caused by thecombined effects of lunar and solarbulges(29½ days) About every 7 days, Earth alternates between– Spring tide Alignment of Earth-Moon-Sun system (syzygy) Lunar and solar bulges constructively interfere Large tidal range– Neap tide Earth-Moon-Sun system at right angles (quadrature) Lunar and solar bulges destructively interfere Small tidal range Time between two successive spring (neap)tides is one half of the lunar cycle (about two

Earth-Moon-Sun positions andthe monthly tidal cycleEffect of declination The plane of theMoon’s orbit istilted 5º withrespect to theecliptic Together withEarth’s tilt of 23.5º, the center of thetidal bulges maybe up to amaximum of 28.5ºfrom the EquatorFigure 10-11Predicted idealized tidesFigure 10-17 Moon goesthrough onecomplete cycle inFigure 10-15: Maximum declination oftidal bulges from Equator. See also Fig.10-14Effect of elliptical orbitsFig. 10-16. Orbits are not exactly circular, but elliptical. Moon hasa stronger tide-generating force when it is in the Perigee (point closestto earth). Equally, the sun has its strongest tide-generating force in theperihelion (January).

Summary of tides on anidealized EarthBut.reality hits in for the tides:Dynamic theory of Tides Most locations have two high tides and twolow tides per lunar day Neither the two high tides nor the two lowtides are of the same height because of thedeclination of the Moon and the Sun (exceptwhen they are above the equator which israre!!) Yearly and monthly cycles of tidal range arerelated to the changing distances of the Moonand Sun from Earth Each week, spring and neap tides alternate,thus in a lunar month there are two springand neap tides.Tides in the oceanFigure 10-18 Tidal bulges are wave crests of waves with awavelength of 20,000km (half of circumference ofEarth) They are shallow water waves (of course) so theirspeed is determined by water depth and is around700km/h, not fast enough to keep up with Earth’srotation Waves break up into cells with centers calledamphidromic points. Wave crests and troughsmove around these points counterclockwise in NHand clockwise in SH So, Coriolis effect and the shape of the oceanbasins influence the location and distribution of theamphidromic points Cotidal mapshows tidesrotate aroundamphidromicpoints Each line shownthe time of themain lunar hightide in lunarhours Tidal rangesincrease withincreasingdistance fromamphidromicpoints Make onerotation in onetid li d (12 hTides in the ocean

Tidal patternsTidal patterns in the U.S.Figure 11-18 Diurnal– One high and one low tide each (lunar) day Semidiurnal– Two high and two low tides of about thesame height daily Mixed– Characteristics of both diurnal andsemidiurnal with successive high and/or lowtides having significantly different heightsMonthly tidal curvesThe Bay of Fundy: Site of theworld’s largest tidal range Tidal energy is focused byshape and shallowness ofbayMaximum spring tidalrange in Minas Basin 17meters (56 feet)Figure 10-25See Figure 10-21

Coastal tidal currents Tidal currentsoccur in somebays and riversdue to a change intides Wall of water thatmoves upriver Caused by anincoming high tide Occurs in somelow-lying rivers Can be largeenough to surf orraft– Ebb currentsproduced byoutgoing tides– Flood currentsproduced byincoming tidesFigure 10-25Grunion and the tides Grunion are theonly fish that comecompletely out ofwater to spawnTidal bore a true tidal wave Spawning cycles are timedprecisely with the tidesFigure 11ASee Fig. 11-26

Tide-generating forces Tide-generating forces are the horizontal component of the resultant force Maximized along a “latitude” of 45º relative to the “equator” between the zenith and nadir Figure 10-7 Tide-generating Tidal bulges forces produce 2 bulges: 1. Away from Moon on side of Earth opposite Moon 2. Toward Moon on side .